Sobre teoremas do tipo Tverberg

Abstract

The main objective of this work is to prove Tverberg-type theorems and related results. More specifically, we will present an alternative proof for the Bárány-Larman conjecture for the case $r = p-1 $ with $ p $ a prime, we prove generalized versions of the colorful Tverberg theorem and a parameterized version of the Borsuk-Ulam- Bourgin-Yang theorem for the case $G=\mathbb{Z}_{p}^m$ or $G=(\mathbb{S}^1)^m$ which is related to the Tverberg-Vre\'{c}ica conjecture.